2006
DOI: 10.1016/j.jalgebra.2006.01.009
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Representation theory of towers of recollement: Theory, notes, and examples

Abstract: We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb algebras. We demonstrate the utility of our formalism by applying it to this class.

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Cited by 38 publications
(83 citation statements)
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“…After reviewing the definition of the Brauer algebra, we will show that families of such algebras form towers of recollement in the sense of [CMPX06] (which we will see follows from various results of Doran et al [DWH99]). This will be the framework in which we base our analysis of these algebras.…”
Section: Preliminariesmentioning
confidence: 80%
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“…After reviewing the definition of the Brauer algebra, we will show that families of such algebras form towers of recollement in the sense of [CMPX06] (which we will see follows from various results of Doran et al [DWH99]). This will be the framework in which we base our analysis of these algebras.…”
Section: Preliminariesmentioning
confidence: 80%
“…To prove these results we use the theory of towers of recollement developed in [CMPX06]. This approach is already closely modelled, for , in work of Doran, Wales, and Hanlon [DWH99] (since both papers use the methods developed in [Mar96]).…”
Section: Theorem 73 (Summary) For Any Integral and Natural Number Amentioning
confidence: 99%
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“…In this section we study B m,p,n via Clifford theory. By verifying the first two conditions of a tower of recollement, we deduce conditions under which the algebra is quasi-hereditary; we leave it as an exercise for the reader to check that the algebra is a tower of recollement (in the sense of [CMPX06]) by checking that it obeys the remaining conditions. 3.1.…”
Section: Brauer Algebras Of Type G(m P N)mentioning
confidence: 99%
“…The idempotent e n−2 (for n = 6) in the cases that δ = 0, δ = 0 respectively. A tower of recollement was defined in [CMPX06] to be a family of algebras (with idempotents) satisfying six conditions (A1-6). It is easy to see that (3.1.1) e n−2 B m,p,n e n−2 ∼ = B m,p,n−2 and that (3.1.2) B m,p,n /B m,p,n e n−2 B m,p,n ∼ = kG(m, p, n).…”
Section: Brauer Algebras Of Type G(m P N)mentioning
confidence: 99%